Construction of optimum space-time convolutional codes based on cyclic codes over groups and fields

In this paper we propose the construction of optimum space-time convolutional codes over groups and fields for quasi-static flat fading channels. These codes are constructed from cyclic codes in order to generate the trellis codes. The space-time convolutional codes over groups are constructed from cyclic group codes based on the solution of the quadratic forms associated with the lattices Z² and A₂. The space-time convolutional codes over fields are found from the construction of maximum distance separable Reed-Solomon and BCH codes whose generator polynomials do not contain any binary factor.